Nonlinear optimal control of spacecraft approaching a tumbling target

This paper investigates the control of spacecraft to approach to and align with a tumbling target. The potential application is to perform on-orbit autonomous satellite servicing. In order to complete the task, the spacecraft is required to perform large position and attitude maneuvers with sufficient accuracy. In addition, the flexible motion induced by large angular maneuvers needs to be minimized. The primary contribution of this work is to consider the control of position and attitude of rigid body and suppression of flexural deformation in one optimal control framework. The 6-DOF rigid body dynamics and coupled flexible structure dynamics are highly nonlinear and lead to a challenging control problem. The θ–Dθ–D nonlinear optimal control technique is employed to design a closed-form feedback controller for this problem by finding an approximate solution to the Hamilton–Jacobi–Bellman (HJB) equation through a perturbation process. The closed-form controller offered by this approach is easy to implement onboard especially for this problem with a large state-space. Numerical results show that the proposed controller exhibits good tracking performance even under large moment of inertia uncertainties.